Torque Self-Test: The Right Hand Rule
Recall \(\tau = r\times F = r F \sin \theta\)
In both diagrams (parts a and b), the force vector F can be thought of as having acted on the arrowhead of moment arm r. However, F has been translated (moved) so that the two vectors are tail-to-tail. This was done in order to simplify the problem.
Part A
In the following diagram, use the right hand rule to find the direction of torque.
The direction of torque is:
- A. into the screen
- B. out of the screen
- C. to the left
- D. to the right
- E. upwards
- F. downwards
- A. No. The tourque cannot be in the plane of the other two vectors.
- B. Correct
- C. No. The tourque cannot be in the plane of the other two vectors.
- D. No. The tourque cannot be in the plane of the other two vectors.
- E. No. The tourque cannot be in the plane of the other two vectors.
- F. No. The tourque cannot be in the plane of the other two vectors.
Part B
In the following diagram, in which direction is the torque?
The direction of torque is:
- A. into the screen
- B. out of the screen
- C. to the left
- D. to the right
- E. upwards
- F. downwards
- A. Correct
- B. No. Remember it is F rotated into r.
- C. No. The tourque cannot be in the plane of the other two vectors.
- D. No. The tourque cannot be in the plane of the other two vectors.
- E. No. The tourque cannot be in the plane of the other two vectors.
- F. No. The tourque cannot be in the plane of the other two vectors.
Recall that = r x F, (or = r F sin) and that the Right Hand Rule says that the thumb points into the direction of torque when the fingers curl in the direction of the cross product (ie. from r to F). Furthermore, the symbol represents a vector going into the screen, while is a vector pointing out of the screen.
Part A
In the first problem, you would point your fingers in the direction of r (left-ward), and 'curl' them upwards (into the direction of F). Your thumb should point into the screen. (Be sure you are using your right hand.)
Part B
In the second problem, r points to the right, so point your fingers to the right. Now 'curl' them upwards, in the direction of F. Your thumb should point out of the screen.